It begs the question though, what did Vito think that Sollozzo had 'under his fingernails'? The only thing I can surmise is that Vito may have thought that someone more big time than Tattaglia was pulling the strings behind the scenes and he wanted to see which of the other families were putting in on the deal besides the Tattaglias.
That is a logical assumption, jrp:
Vito told Michael (and presumably, Tom): "Think as others around you think." If Vito (and Tom) had been thinking strategically, they would have concluded that Sol needed three things: the credibility of working with one of the Five Families; a lot of working capital, and police/political protection. But Sol had something big to give in return: the money his partner earned with him through drugs would buy more police/political protection, making the partner stronger.
Vito had everything Sol needed, but Vito was already on top with businesses that were a lot less risky than Sol's. So, Sol might first have contacted Barzini, who he knew was younger than the other Dons, more ambitious, thinking of himself as
Capo di Tutti Capi in waiting. Barzini would have heard him out and replied: "Your logic is good. But you still need Corleone's police/political protection. If he hears that I'm backing you, he'll say no. Go to Tattaglia--he's a pimp; Corleone isn't worried about him. Tell Tattaglia and Corleone anything you want, but I'll be your real partner--your silent partner--I'll have your back at all times."
If Vito (and Tom) were in their think-as-others-around-you-think mode, they'd have smelled a rat. But they weren't in that mode. In fact, it's amazing that it took Vito until after the Commission meeting to figure out that "it was Barzini all along."
